This claim that the United States can exploit its own oil and gas resources to power 60 million cars and heat 160 million houses for the next 60 years is indeed bold.

Not really. A better word would be "irrelevant".

60 million cars sounds like a lot, until you realize that there are 250 million cars in the US. So if somebody's talking about a wholly arbitrary number like 60 million, you should be curious about what their agenda is.

At 250 million cars, that 60 years is down to 14, which doesn't sound quite as impressive.

Much the same sleight of hand is being done with their natural gas figure. 160 million households sounds like a lot - and it is - until you realize that households consume only 1/3 of natural gas in the US.

Is it true, does humanity have many generations to slowly perfect beyonf fossil fuel energy sources?

Probably not, but neither is it likely the process will take many generations. The requisite technologies are advanced enough that a changeover within a generation is entirely possible, with a few small exceptions (air and possibly sea travel).

At 250 million cars, that 60 years is down to 14, which doesn't sound quite as impressive.

Nobody knows what the crisis of high fuel prices will get the number of cars down to. the number of cars is not that relevant it's how many are on the road at a given time and etc.

If the number of cars isn't relevant, then why would the person saying "60 million for 60 years!" mention them?

Point is, it's a dodgy claim.